Military question

So I'm just rewatching the Stargate movie, and since I know better than to trust Hollywood for (American) military accuracy, a question:

Would anyone, officer or enlisted man, be chewing gum while on duty in their dress uniform? I know the military has many, many regulations on appearance and behavior while on duty, but do they address gum chewing? How about cigarette smoking?

So many irrelevant questions, so little patience for Google...